Robin Neumayer University of Texas at Austin Title: A strong form of the quantitative Wulff inequality

Abstract: For a set $E$ that almost minimizes perimeter among sets of the same volume, quantitative isoperimetric inequalities measure how close $E$ is to the unique perimeter minimizer. A recent paper of Fusco and Julin gives a quantitative isoperimetric inequality where the deficit in the inequality controls the oscillation of the boundary of $E$. In this talk, we will generalize this result to the anisotropic case, where perimeter is weighted with respect to some fixed convex set $K$.